Answer:
the Area is approximately 1
Step-by-step explanation:
Since
y=x^3
the area under a curve can be approximated to rectangles of width Δx and length y , then
Area = Sum of rectangles of width x and length = ∑ y *Δx
taking the width Δx=1 for each rectangle
Area = Sum of rectangles of width x and length= ∑ y = ∑ x^3
from x=0 to x=1 , there is only one rectangle of width Δx=1 , then
since ∑ x^3 from x=0 to x=n is n(n+1)/2]^2
Area = ∑ x^3 from x=0 to x=1 = 1(1+1)/2]^2 = 1
Note:
- The actual value of the area is calculated through the integral
Area= ∫ y dx = ∫ x^3 dx from x=0 to x=1 = 1⁴/4 = 1/4